Download question2_sol

Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
Problem/Question of the Day
Distributed: 7/21/14
Due in Class: 7/22/14
1. Consider the market for economics textbooks (You don’t have to worry about whether the
prices and quantities are reasonable). Let qD = 40-0.5P represent the demand curve for an
individual consumer, and qS = -80+4P represent the supply curve for an individual producer.
Furthermore, assume that there are 100 identical consumers and 5 identical producers in the
market. The quantity units are books and the currency is US dollars.
a. Plot the individual consumer demand curve and individual firm supply curve on
separate graphs. (Graphs do not have to be to scale or on graph paper, but please label
the important features- intercepts, etc.)
b. What are the equations for the market supply and demand curves? Please plot market
demand and supply on the same graph. How do these curves compare to those for
individual supply and demand?
Because all of the individuals are identical, if one individual demands qD books,
then 100 people demand 100*qD books. Multiplying the right hand side of our
individual demand equation by 100, we get: QD = 4000-50P. For firms, since they
are also identical, if one firm supplies qS books then 5 firms supply 5* qS books.
Thus, we get: QS = -400+20P. You can also think of this as horizontal addition...
You should get this graph:
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
As for how these compare to individual supply and demand, the graphs for
market supply and demand are stretched horizontally, i.e. along the quantity
axis. The P-axis intercepts stay the same, but the slope of the lines is different.
c. What is the equilibrium price and quantity in the market for books?
To solve here we need to set QS=QD - using the equations we solved for above we
have:
QD = 4000-50P and QS = -400+20P
So 4000-50P=-400+20P --> 4400=70P --> P=440/7, so price is $62.86 USD.
To find quantity we can just plug this P value back into wither of the two
quantity expressions:
QD = 4000 - 50(440/7) = 4000-3143 = 857 books
So P = $6,286 and Q = 857 books in equilibrium.
d. If an individual’s income rises, will he demand more or fewer books? What
assumption (in economic terms) did you make to reach this conclusion?
He will likely demand more books. The assumption that I made was that books
are a normal good, in which case demand goes up as income rises. You could
also argue that books are inferior goods, in which case the opposite would be
true (less income would lead to a greater demand), because the individual does
not want to learn more economics but consumes income in other (better?) ways.
It’s a bit of a judgment call.
e. If the price of hardcover fiction books falls, what happens to the demand for
paperback fiction books? Why? If the price of electricity rises, what happens to
demand for books? Why?
Instructor: Akos Lada
Harvard Kennedy School
Mid-Career MPA
Summer Program 2014
If the price of hardcovers falls, the demand for paperbacks decreases. This is
because the two are substitutes, so as the price of hardcovers goes down the
demand for paperbacks goes down too. If the price of electricity rises, the
demand for paperback is (virtually) unchanged, since they are unrelated goods.
(You could argue that if demand for electricity is very inelastic, there would be
less money left over for other goods, but this is a minor effect. Or that people
read by electric light. On the other hand, maybe consumers use their TV less and
read instead. The important point is that electricity and paperbacks are
considered neither substitutes nor complements.)
f.
Suppose that the fiction writers’ union recently negotiated higher wages. What
happens to the supply of paperbacks? Explain.
Wages are an input price. Input prices are a determinant of supply, and when
input prices go up, supply goes down. Therefore the supply of books goes down
(decreases).
g. Now suppose that consumer groups lobbied the government to pass a bill to keep the
price of paperbacks lower than the equilibrium price. What type of price control
would they want to lobby for? What would result, economically speaking, from such
a price control if it was passed and enforced?
They would want a price ceiling set below the market equilibrium price.
However, such a binding price ceiling would lead to excess demand and
insufficient supply - in other words, a shortage.
h. Suppose the price control in part (g) was passed at a price of $50. What would be the
resulting price and quantity consumed in the market? What would be the amount of
shortage/surplus?
With a price ceiling of $50, the quantity demanded and supplied would be:
QD = 4000-50P with P=50, so QD = 1500
QS = -400+20P with P=50, so QS = 600
So we can see here that there is a shortage, as expected. 1500 books are
demanded but only 600 are supplied. There is a shortage of 900 books. The
market price would be $50 and the market quantity would be 600 books.